Continuing our project on noncommutative (stable) homotopy we construct symmetric monoidal -categorical models for separable -algebras and noncommutative spectra using the framework of Higher Algebra due to Lurie. We study smashing (co)localizations of and with respect to strongly self-absorbing -algebras. We analyse the homotopy categories of the localizations of and give universal characterizations thereof. We construct a stable -categorical model for bivariant connective -theory and compute the connective -theory groups of -stable -algebras. We also introduce and study the nonconnective version of Quillen's nonunital -theory in the framework of stable -categories. This is done in order to promote our earlier result relating topological -duality to noncommutative motives to the -categorical setup. Finally, we carry out some computations in the case of stable and -stable -algebras.
Cite this article
Snigdhayan Mahanta, Symmetric monoidal noncommutative spectra, strongly self-absorbing -algebras, and bivariant homology. J. Noncommut. Geom. 10 (2016), no. 4, pp. 1269–1301DOI 10.4171/JNCG/260